Mayor Bill de Blasio, Council Speaker Melissa Mark-Viverito, and members of the City Council announce an early agreement for an on-time and balanced City budget for Fiscal Year 2016. City Hall, New York on Monday, June 22, 2015. (Credit: Mayoral Photography Office/ Demetrius Freeman)

Mayor Bill de Blasio's relationships with Gov. Andrew M. Cuomo and City Council Speaker Melissa Mark-Viverito have been tested in recent weeks, but he categorized them as "apples and oranges" Monday in an appearance alongside the speaker.

Mark-Viverito, in a rare rebuke of de Blasio Thursday, criticized his administration for neglecting to give the City Council more credit in brokering a truce with Uber after initially threatening to cap the e-hail giant's growth.

Cuomo and de Blasio earlier this month feuded openly over what the mayor perceived to be the governor's thwarting of New York City's agenda in Albany.

"Have you heard of the concept of apples and oranges?" de Blasio said Monday when asked to compare the feuds.

On Thursday, Mark-Viverito had said: "I'm not going to allow anyone to attempt to save face at the expense of this council." She added that de Blasio's statement then that a moratorium was still on the table was "really not for him to decide."

On Monday, she and the mayor were on friendly terms at a news conference at the American Museum of Natural History lauding a successful first six months for the IDNYC city-issued identification program. They had more diplomatic words for each other.

"Effective government and effective governance is being able to collaborate and being able to be clear about your positions," Mark-Viverito said. She and de Blasio had a "good working relationship," in the best interest of the city, she said.

De Blasio in turn said he and the speaker have worked "shoulder to shoulder" in the 19 months since they were voted into their respective positions.

"It's been a respectful, honest relationship," he said, acknowledging what Mark-Viverito indicated last week that he had overlooked: "The City Council makes their own decision ultimately about whether to engage any proposal."

The council had been poised to vote on two bills to launch a 14-month traffic study into the rapidly expanding Uber and similar services, while capping Uber's growth at 1 percent. Instead -- following an agreement announced by de Blasio's team -- the council voted on a four-month study with the app-dispatched livery service permitted to expand at its current rate.

"The city government" came to the agreement, the mayor stressed on Monday.

His partnership with Cuomo was another matter, a "very different reality based on different experiences," de Blasio said.

Asked whether he was invited to an Association for a Better New York-hosted luncheon later in the afternoon in midtown Manhattan with Cuomo and Vice President Joe Biden, de Blasio said only: "That's the kind of event that I go to when I'm speaking, but not obviously as an attendee."

Mark-Viverito attended the event with Cuomo.

De Blasio openly criticized Cuomo earlier this month, telling reporters that anyone who wronged the governor was subjected to revenge or a "vendetta."

Cuomo had responded that de Blasio spoke out because he didn't get everything he wanted from the legislative session. The mayor needed to seek bipartisan compromise to get more of what he wanted, Cuomo said. "Welcome to Albany," the governor said.